No... they are provided in your room (usually the towel art on your bed is the beach towels for you)... there will be two and you can exchange for fresh ones anytime during your stay, as many times as you need.

Then on your last nite there, go turn them in to the watersports shack and they will give you a receipt that you'll need to present up checkout.

No, there will be 2 in your room. You can swap them out at the beach if you want clean ones during the day and you can actually get extras at the beach. Well, that is you can at Couples Negril and Swept Away.